Phase transitions induced by saddle points of vanishing curvature

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dc.creatorKastner, Michael
dc.creatorSchnetz, Oliver
dc.date2007-11-06
dc.date2008-04-25
dc.date.accessioned2026-07-07T09:34:48Z
dc.date.available2026-07-07T09:34:48Z
dc.descriptionBased on the study of saddle points of the potential energy landscapes of generic classical many-particle systems, we present a necessary criterion for the occurrence of a thermodynamic phase transition. Remarkably, this criterion imposes conditions on microscopic properties, namely curvatures at the saddle points of the potential, and links them to the macroscopic phenomenon of a phase transition. We apply our result to two exactly solvable models, corroborating that the criterion derived is not only valid, but also sharp and useful: For both models studied, the criterion excludes the occurrence of a phase transition for all values of the potential energy but the transition energy. This result adds a geometrical ingredient to an established topological condition for the occurrence of a phase transition, thereby providing an answer to the long standing question of which topology changes in configuration space can induce a phase transition.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/0711.0852
dc.identifierhttp://arxiv.org/abs/0711.0852
dc.identifierPhys. Rev. Lett. 100, 160601 (2008)
dc.identifierdoi:10.1103/PhysRevLett.100.160601
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159621
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.titlePhase transitions induced by saddle points of vanishing curvature
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